Some Logical Basics

Principle of Sufficient Reason For every truth or thing that exists, there is a sufficient reason or explanation for its being true or existing, rather than otherwise. Truths have an explanation, existing things have a reason for their being. Events do not occur, things do not come to exist, and truths do not come to be ex nihilo or from nothing; there is always an explanation behind them.

Logical Possibility Any proposition whose opposite does not imply a contradiction is logically possible. That is, if the sentence does not include a contradiction like, "Mike is a married bachelor." then the state of affairs that the sentence describes is logically possible. So it is log. poss. that Mike is a bachelor. And it is logically possible that he is married. And it is logically possible that Mike (an unaided human) could fly. But it is not logically possible that 2 + 2 = 5, or that circles have sides, or that the Pythagorean Theorem is wrong, etc.

Natural Possibility The laws of nature such as the universal law of gravitation, F = MA, and e=mc2 determine the range of what states of affairs are naturally possible. So it is not naturally possible for an unaided human body to fly—the musculature, bone structure, and other physiological traits prevent it. But it is naturally possible (we think) to cure cancer. The laws of nature, which are different from the laws of logic, could have been different without logical contradiction. The periodic table could have been different, gravity could attract at a different rate, or force could be equal to something different than mass times acceleration. If one of those different sets of natural laws were in place, then the range of what events that is naturally possible would be different.

A necessary truth is one whose opposite implies a contradiction. It is a proposition that must be true without exception. A = A is a necessary truth, as is "Bachelors are unmarried," and "Triangles have three sides." A necessary being is one whose non-existence is impossible. That is, a necessary being must exist; it cannot fail to exist. God is the only being typically characterized as a necessary being.

A contingent truth is one that can be true or it can be false without logical contradiction. "George W. Bush is the president" could have been false without violating the law of non-contradiction. He might have only been a gas station attendant. A contingent being is one that could have existed or could have not existed without logical contradiction. We humans are all contingent.

The Law of Non Contradiction It is not possible for a thing to both possess and not possess a property at the same time in the same way. To make an assertion of the form X is P, like the ball is blue, is to claim that the ball has the property of blue and that it is false that the ball is non-blue. If we abandon the law of non-contradiction, then there is no meaningful difference between an assertion and its opposite. That is, our assertions cease to have meaning altogether. My claim that, "Today is Tuesday," doesn't say anything unless it denies some other state of affairs like, "Today is Wednesday." The law of non-contradiction is axiomatic to reason; that is, it is one of the most fundamental principles upon which reasoning and rationality are based. It cannot be argued for (it is the principle that makes arguments possible) nor can in be plausibly denied (to deny it is to already assume it.)

A priori truths are truths that can be known without an appeal to experience. They are true by definition or in virtue of the meanings of the words involved. "A square is a four sided figure," is an a priori truth. We do not need to count the sides of objects that are squares in the world to know that it is correct. "Mammals have warm blood," is another a priori truth.

A posteriori truths are truths that we discover and know on the basis of experience. "McCormick is 6' 1" tall," is a fact that can only be discovered by experience. It cannot be known by conceptual analysis the way "bachelors are unmarried" can. "Interest rates were at a 40 year low in July" is another example of an a posteriori truth.

Belief To believe a claim is to assent to it or to have an attitude towards it such that you think it is true. It may or may not be true, but to believe it is to think that it is. So many people believed that the earth is flat. Some may still believe it. Belief is subjective because it is dependent upon an individual to possess it. Belief is mind dependent.

Truth The truth is what is the case or what the actual state of affairs in the world is. We form beliefs about it on the basis of our information. The truth is objective—it does not depend upon people. Truth is mind-independent. It remains what it is whether we form beliefs about it or not. When people believed that the earth was flat, in fact, it was not. The truth was that the earth was (and is) spherical.

Natural Theology is the project of attempting to give a successful argument (see below) for the existence of God. Natural theologians, such as William Paley, Aquinas, Anselm, and Craig, believe that reasons can be given that are adequate to make the conclusion that God exists reasonable or justified.  Natural theologians are usually not opposed to faith, but they believe that reasonable belief in God can be secured without necessarily appealing to it. 

A Successful Argument for a conclusion (call it C) will be a set of premises or reasons (different than C) that are true and that when taken jointly would imply the conclusion C to a reasonable person who does not already believe C.  A prosecuting attorney in a murder trial will attempt to give a successful argument that will convince the jury (who has assumed the defendant's innocence) that the defendant is guilty.  So a reasonable person should accept the conclusion of a successful argument. Of course, people rarely hear a convincing argument and then abruptly change their minds.  But reasonable people should be prepared to. If you hear an argument with premises that you beleive are true, and you understand that the premises validly imply the conclusion, then you are rationally committed  to accept the conclusion.  Otherwise, you are being irrational.  Disagreements about whether or not an argument is successful will be disagreements about whether or not all of the premises are true or whether or not the premises, if true, would imply the truth of the conclusion. 

Faith is a description of a way that people sometimes acquire beliefs.  For S to believe p by faith means that S believes p despite the fact that as S sees it, there is contrary evidence or inadequate evidence overall to make p justified.  When someone says, "I have faith that my team will win the playoffs even though they are 3 games behind," they are saying that there are significant reasons to doubt the truth of the claim, but they believe it nevertheless.  (See belief above.)  Consider a parent who is worrying about her child who is dying from leukemia. She might say, "Why would God allow such a thing to happen to someone who is so innocent?"  The hospital chaplain might reply, "We must have faith that God has a plan for such events."